In unit-vector notation, what is the net torque about the origin on a flea located at coordinates (0, -4.0 m, 5.0 m) when forces

$${\overrightarrow{F_1}} = (3.0\ N){\hat{k}}$$

and

$${\overrightarrow{F_2}} = (-2.0\ N){\hat{j}}$$

act on the flea?

As part of a circus act, a person drives a motorcycle with constant speed $v$ around the inside of a vertical track of radius $r$, as indicated in the given Figure. If the combined mass of the motorcycle and rider is $m$, find the normal force exerted on the motorcycle by the track at the point B.

The strong force (select all that apply) a) is only attractive. d) All of the above are true. b) does not act on electrons. c) only acts over a few fm. d) All of the above are true. e) None of the above are true.

The words listed below appear in The Tragedy of Julius Caesar. Act $V$. Use one word from the list to write a complete sentence about each numbered item that follows. fawned presage demeanor disconsolate meditates

watching the sun set

A force $\overrightarrow{\mathbf{F}}=F \hat{\mathbf{j}}$ is applied to an object at a position $\overrightarrow{\mathbf{r}}=x \hat{\mathbf{i}}+y \hat{\mathbf{j}}+z \hat{\mathbf{k}}$ where the origin is at the cM. Does the torque about the cm depend on $x$ ? On $y$ ? On $z$ ?

A force $(2.00 \hat { i } - 4.00 \hat { j } + 2.00 \hat { k })N$ acts on a particle located at $( 3.00 \hat { i } + 2.00 j - 4.00 \hat { k } ) m$. What is the magnitude of the torque on the particle as measured about the origin?

The rotor is an amusement park ride where people stand against the inside of a cylinder. Once the cylinder is spinning fast enough, the floor drops out. (a) What force keeps the people from falling out the bottom of the cylinder? (b) If the coefficient of friction is 0.40 and the cylinder has a radius of 2.5 m, what is the minimum angular speed of the cylinder so that the people don't fall out? (Normally the operator runs it considerably faster as a safety measure.)

If the initial rotational velocity of the merry-go-round was $1.2 \mathrm{rad} / \mathrm{s}$, what is the rotational velocity after the children move in toward the center, assuming that the frictional torque can be ignored? (Use conservation of angular momentum.)

Two forces of the same magnitude $F_1$ and $F_2$ act at angles $\theta_1$ and $\theta_2$ respectively. Compare the work done by $F_1$with the work done by $F_2$ in moving along the vector $\overrightarrow{PQ}$ if

$\theta_1=60^\circ$ and $\theta_2=30^\circ$

As Collins in "The Mystery of Heroism", write a letter to a friend or a relative in civilian life. Explain your views about war, your relationship with your comrades, your act of "heroism," and what you learned from your brush with death.

Add commas where necessary. Cross out commas used incorrectly by using the delete symbol. Some sentences may be correct. Angie read aloud the opening lines of act I, scene ii, of Shakespeare's Julius Caesar.

After listening to the Ghost speak, Hamlet wants to write about it, as indicated in act I, scene v, lines 107 and 108. How does this contrast with his remarks earlier in this speech? What does it suggest about his state of mind?

The shaft rotating at $200\ \mathrm{rpm}$ carries a 6-in-diameter chain sprocket $D$ that delivers $4\ \mathrm{hp}$ to a mating sprocket above. Compute the torque delivered by the shaft to sprocket $D$ and the force exerted on the shaft by the sprocket.

Compute the required diameter for a solid circular shaft if it is transmitting a maximum of $110\ \mathrm{hp}$ at a speed of $560$ $\mathrm{rpm}$. The torque varies from zero to the maximum. There are no other significant loads on the shaft. Use SAE 4130 WQT 700.